Scheduling method with tunable throughput maximization and fairness guarantees in resource allocation

ABSTRACT

A flexible scheduling method with tunable throughput maximization and fairness guarantees in resource allocation is required and suitable for high-rate packet data and other services. Our inventive method, named Alpha-Rule, employs a control variable α, that permits dynamic and/or real-time adjustment/tradeoff between aggregate throughput, per-user throughput, and per-user resource allocation. Our method advantageously operates in conjunction with Multiple-input Multiple-Output techniques such as Space-Time Block Coding (STBC), Bell Labs Layered Space-Time (BLAST) and others, while offering greater flexibility than existing scheduling techniques, e.g., max-C/I or Proportionally Fair (PF).

FIELD OF THE INVENTION

This invention relates generally to the field of wirelesscommunications, and in particular to method(s) for scheduling exhibitingtunable throughput maximization while providing fairness guarantees inresource allocation.

BACKGROUND OF THE INVENTION

High-speed downlink packet data services are of importance to thesuccess of third-generation (3G) and beyond, wireless systems. Examplesof such systems include CDMA2000 (see, e.g., 3GPP2 C.S0024 Version 4.0,CDMA2000 High Rate Packet Data Air Interface Specification, December2001); the High Data Rate (HDR) system which is described in an articleentitled CDMA/HDR: a bandwidth-efficient high-speed wireless dataservice for nomadic users, that was authored by P. Bender et al., andappeared in IEEE Communications Magazine, pp. 70-77 in July 2000; HighSpeed Data Packet Access (HSDPA) as described in the 3GPP TechnicalSpecification 25.308 version 5.2.0, entitled High Speed Downlink PacketAccess (HSDPA): Overall Description, published in March 2002. As isgenerally known, each of the systems employs Time-Division MultipleAccess (TDMA) techniques to provide sharing of a downlink data channelamong multiple users.

To facilitate the deployment and effectiveness of such systems,supporting technologies, such as transmission techniques and schedulingmethods are being explored and characterized. Specifically, at thephysical layer, Multiple-Input Multiple-Output (MIMO) antenna techniquesare attractive because they can increase the channel capacity between abase station (BS) and an individual user due, in part, to the spatial(antenna) diversity. At the media access control (MAC) layer, ascheduler within the BS selects users for transmission according totheir channel-state-information (CSI) feedback and their measuredthroughput performance, characterizing their multiuser diversity as wasdescribed by M. Grossglauser and D. Tse, in an article entitled“Mobility increases the capacity of ad hoc wireless networks”, whichappeared in IEEE/ACM Trans. Networking, Vol. 10, No. 4, pp 477-486 inAugust 2002.

As can be appreciated, both types of diversity identified above play acentral role in systems that exhibit high throughput and fair resourceallocation among users.

Multiple-Input Multiple Output (MIMO) antenna techniques, (see, e.g., S.M. Alamouti, “A Simple Transmit Diversity Technique for WirelessCommunications”, IEEE J. Select. Areas Commun., vol 16, No. 8, pp.1451-1458, Oct. 1998; G. J. Foschini, “Layered Space-Time Architecturefor Wireless Communication In a Fading Environment When UsingMulti-Element Antennas”, Bell Labs Technical Journal, vol. 1, No. 2, pp.41-59, Autumn 1996; and I. E. Telatar, “Capacity Of Multi-AntennaGaussian Channels”, European Trans. On Telecommun., vol 10, pp. 585-595,November-December 1999). One of these techniques, Orthogonal Space-TimeBlock Coding (STBC) was recently adopted for implementation as one ofthe transmission diversity modes in 3G wireless networks (See, forexample, V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-TimeBlock Codes From Orthogonal Designs”, IEEE Trans. Inform. Theory, vol.45, no 5, pp. 1456-1467, July 1999). The STBC technique advantageouslyachieves “full transmit diversity” and reliable channel(s), however itdoes not exhibit particular transmission efficiency.

Another technique, the Vertical Bell Labs Layered Space-Time (V-BLAST)technique, which was described in a paper authored by P. Wolniansky, G.J. Foschini, G. D. Golden, and R. A. Valenzuela entitled “V-BLAST: AnArchitecture For Realizing Very High Data Rates Over the Rich-ScatteringWireless Channel” which appeared in Proc. Int. Symp. Sig. Sys. Elect.(ISSSE), in Pisa, Italy in September 1998 and another paper authored byG. J. Foschini, G. D. Golden, R. A. Valenzuela and P. W. Wolniaskyentitled “Simplified Processing For High Spectral Efficiency WirelessCommunication Employing Multi-Element Arrays”, that appeared in IEEE J.Select. Areas. Commun., vol 17, No 11, pp. 1841-1852 and published inNovember 1999, provides high-rate data transmission but is less reliableduring instantaneous deep fades.

Scheduling methods, and in particular scheduling methods for selecting aparticular user to whom access to a system should be granted havelikewise been the subject of much investigation. More specifically,certain methods grant access to the user that can most efficiently usethe system—the one with the best/strongest channel thereby having thehighest data rate. In such systems, throughput is maximized at theexpense of users using less desirable channels. One such system, wasdescribed in U.S. Pat. No. 6,449,491 for Transmitter Directed CodeDivision Multiple Access System Using Path Diversity To EquitablyMaximize Throughput which issued to Chaponniere et al on Sep. 10, 2002,determined an access metric for each user and provided channel access tothat user having the greatest access metric.

Alternative scheduling methods have been explored that provide channelaccess to all users equally—regardless of channel efficiency orthroughput. With such systems, the equal access—which may be based ontime/duration or volume of transmission—sacrifices overall systemefficiency for equality of access.

In addition, methods such as the Maximum Carrier-to-Interference Ratio(max-C/I) scheduling which was described by R. Knopp and P. A. Humbler,in a paper entitled “Information Capacity and Power Control in SingleCell Multiuser Communications”, which appeared Proc. IEEE Int. Conf.Commun. (ICC), at pp. 331-335, in June 1995; the Proportionally Fair(PF) scheduling method as described in a paper entitled “Data Throughputof CDMA-HDR A High Efficiency-High Data Rate Personal CommunicationWireless System”, authored by A. Jalali, R. Padovani, and R. Pankaj,that was published in Proc. IEEE Veh. Technol. (VTC), at pages 1854-1858in May 2000; and a paper by P. Viswanath, D. N. C. Tse and R. Laroia,entitled “Opportunistic Beamforming Using Dumb Antennas” that appearedin IEEE Trans. On Inform. Theory, vol. 48, No. 6, pp. 1277-1294 in June2002; and the wired, Max-Min Fair scheduling method as described by D.Bertsekas and R. Gallagar in Data Networks, Chapter 6, published byPrentice-Hall of Englewood Cliffs, N.J. in 1992 all offer particularadvantages/disadvantages which characterize their method.

More specifically, each of the above methods differs in the performanceof aggregate downlink throughput and the fairness as it relates toper-user time/throughput. Each (except Max-Min Fair) however, ischannel-dependent in that they all rely on instantaneous CSI feedback asopposed to the simpler, Round-Robin (RR) scheduling where users areselected independently of channel status.

Accordingly, there exists a continuing need for methods that providefair access to users of shared wireless systems, while maintainingoverall system efficiency. Such method(s) is/are the subject of thepresent invention.

SUMMARY OF THE INVENTION

We have developed a method that—in sharp contrast to the priorart—provides access to users of a shared wireless system whileeffectively balancing aggregate throughput and fairness. Our method,which we have named Alpha-Rule, can advantageously migrate between andbeyond the throughput/fairness extremes of the prior art MaximumCarrier-to-Interference Ratio (max-C/I) and Proportionally Fair (PF)methods through the use of our inventive control variable, α.

Viewed from a first aspect, our invention is directed to a method whichdetermines which one of a plurality of users of a shared network haveaccess to a particular timeslot. Specifically, our inventive Alpha-Rulemethod determines which user by the following relationship:$k^{*} = {\arg\quad{\max\limits_{k}\left\{ {w_{k}\frac{r_{k}(t)}{{r_{k}(t)}^{a}}} \right\}}}$

Viewed from another aspect, our invention is directed to a furthermethod of adjusting our inventive Alpha-Rule scheduler, utilizing twocriteria throughput and fairness which are defined respectively as:$r = {\sum\limits_{k = 1}^{K}\quad{\overset{\sim}{r}}_{k}}$ and${F = \frac{\left( {\sum\limits_{k = 1}^{K}\quad x_{k}} \right)^{2}}{K{\sum\limits_{k = 1}^{K}\quad x_{k}^{2}}}},$where x_(k) can be {tilde over (r)}_(k) or the per-user percentage(portion) of resource (time-slot) allocation, denoting per-userthroughput or resource fairness, respectively.

Our evaluation shows that our inventive Alpha-Rule method compensatesfor the deficiencies of both PF and max-C/I, thereby producing a moregeneric and/or flexible scheduling method. Of further advantage, ourAlpha-Rule permits real-time performance tuning as control variable amay be dynamically adjusted to a desired system throughput or fairnesscharacteristic(s).

Additional objects and advantages of our invention will be set forth inpart in the description which follows, and, in part, will be apparentfrom the description or may be learned by practice of the invention.

BRIEF DESCRIPTION OF THE DRAWING

Further objects of the invention will be more clearly understood whenthe following description is read in conjunction with the accompanyingdrawing and figures in which:

FIG. 1 is a block diagram of a downlink transmitter structure at a basestation;

FIG. 2 is a block diagram of a receiver structure at a user terminal;

FIG. 3 is a flow chart depicting the operation of our inventiveAlpha-Rule method; and

FIG. 4 is a flow chart depicting the tuning of the Throughput and (theexemplary per-user throughput) Fairness parameters of our inventiveAlpha-Rule method of FIG. 3.

DETAILED DESCRIPTION

With reference now to FIGS. 1 and 2, there is shown a block diagram of ahigh-speed packet cellular system comprising both a Base Station(FIG. 1) and a User Terminal (FIG. 2), which will serve to describe anapplication of the present invention.

Specifically, and with simultaneous reference to those FIGUREs, shown intherein is a high-speed downlink and corresponding user terminal thatmay, for example, adopt a STBC or BLAST technique(s). Independent ofthese schemes, and as shown therein, the system includes nT transmitantennas and nR receive antennas. The channel is time slotted and anyfading processes between transmitter-receiver pairs, or between the basestation and different mobile users, are assumed to be stationary andergodic.

Returning our attention now to FIG. 1, data bits, from each of the 1 . .. K users, is assumed to be infinite and is buffered at buffers 110[1 .. . K], from which it is subsequently presented to scheduler 120. Afteran appropriate scheduling methodology is applied by the scheduler 120,the scheduled user data is modulated (for example, by QPSK) at modulator130, multiplexed by time-division multiplexer (TDM) 140 with pilotsignal 145, and subsequently encoded by encoder 150 prior totransmission by antenna array 160. As can be appreciated, the specificmodulation, multiplexing, encoding or antenna array is only dependentupon the specific design choice(s) made by the system implementor.Advantageously, our inventive scheduling method is applicable to any ofthe known modulation, multiplexing, or coding methods known and used inthe art.

At the receiver shown in FIG. 2, data transmitted according to thestructure shown in FIG. 1 is received by the η_(R) receive antennas,270[1 . . . K], channel information is determined by channel estimator275, and the corresponding channelized data is decoded by decoder 280,then demodulated by demodulator 285 prior to presentation to aparticular user.

At this point, a mathematical introduction is in order. For the abovesystem(s) of FIG. 1, the received discrete-time signal at the k^(th)terminal out of a total of K such terminals may be modeled by:$\begin{matrix}{{{{r_{k}(t)} = {{\sqrt{\frac{E_{s}}{n_{T}}}H_{k}{c_{k}(t)}} + {n_{k}(t)}}},{t = 1},\ldots\quad,T,{with}}\begin{matrix}{{{r_{k}(t)} = \left\lbrack {{r_{1,k}(t)},{\ldots\quad{r_{n_{R},k}(t)}}} \right\rbrack^{T}};} \\{{H_{k} = \left\lbrack {h_{1,k}^{T},\ldots\quad,h_{n_{R},k}^{T}} \right\rbrack^{T}};} \\{{h_{j,k} = \left\lbrack {h_{{1j},k},\ldots\quad,h_{{n_{T}j},k}^{T}} \right\rbrack^{T}};} \\{{{c_{k}(t)} = \left\lbrack {{c_{1,k}(t)},\ldots\quad,{c_{n_{T},k}(t)}} \right\rbrack^{T}};} \\{{{n_{k}(t)} = \left\lbrack {{n_{1,k}(t)},\ldots\quad,{n_{n_{R},k}(t)}} \right\rbrack^{T}};}\end{matrix}} & \lbrack 1\rbrack\end{matrix}$where

-   -   c_(i,k)(t), i=1, . . . ,n_(T) is the symbol from transmit        antenna i to user k at time slot t;    -   E_(s) is the average total transmission energy in one time slot,        for example, tr(E{c_(k)(t)c_(k) ^(H)(t)})<E_(s);    -   H_(k) is a circularly symmetric complex matrix of dimension        n_(R)×n_(T),    -   h_(ij,k) represents the channel gain from transmit antenna i to        receive antenna j of the k^(th) user, which is a complex        Gaussian random variable with zero mean and variance 0.5 per        dimension; and    -   n_(k)(t) is a complex Gaussian random vector with zero mean and        covariance matrix σ_(k) ² I, i.e., n_(k)(t)˜N_(C)(0, σ_(k) ²I).

Throughout this description of our inventive method, we assume thatspatial paths of different transmitter-receiver pairs are independentdue to the rich scattering experienced in wireless communications.Stated alternatively, h_(ij,k)(∀i,j) are independent of each other. Inaddition, for each complex Gaussian random variable, its real andimaginary parts are also independent and accounts for half of the totalvariance. For example, the real and imaginary parts of n_(k)(t) follow${N\left( {0,{\frac{\sigma_{k}^{2}}{2}I}} \right)}.$

Furthermore, assume that the channel matrix H_(k) is known to thereceiver of each user, but not the transmitter. Accordingly, theinstantaneous capacity of the MIMO channel may be written as:$\begin{matrix}{{{R_{k}(t)} = {{logdet}\left( {I_{n_{R}} + {\frac{\rho_{k}}{n_{T}}H_{k}H_{k}^{H}}} \right)}};} & \lbrack 2\rbrack\end{matrix}$Where $\rho_{k} \equiv \frac{E_{2}}{\sigma_{k}^{2}}$is the mean signal-to-noise (SNR) of user k; H_(k) is the instantaneouschannel state at time t, and the capacity units are bits/s/Hz. Toeliminate any confusion, we eliminate the subscript k whenever possible.

With this background theoretical foundation in place, we now turn ourattention to our inventive scheduling method. As can be readilyappreciated by those skilled in the art, numerous scheduling methodshave been proposed for wired networks, but few offer much applicabilityto the somewhat more complex wireless scenario. The reason(s) for thislimited applicability are numerous.

First, the deterministic, fixed bandwidth capacity constraint for userssharing a wired link is replaced by the highly unpredictable wirelesschannel which exhibits heterogeneous channel statistics for differentusers. Second, the resources in a wireless network such as the timeslots, link capacity and power, are separate and orthogonal resourcesamong different users.

In wired networks in sharp contrast, the sharing of time slots isgenerally equivalent to the sharing of bandwidth, while power is notmuch of a concern. Additionally, with wireless scheduling, per-userthroughput is not equivalent to per-user (time-slot) resourceallocation.

For the purposes of our discussion we only consider the TDM-baseddownlink scheduling where the downlink channel is time slotted, althoughour invention is not so limited. Additionally, for the purposes of thisdiscussion, we assume that in each time slot, at most one user can betransmitting, i.e., there is no code multiplexing. With these principlesin place, we now introduce our inventive Alpha-Rule method and thendemonstrate its generalization to the prior art PF and max-C/Ischeme(s).

We begin by first considering a best-effort high-data-rate packetservice in a cellular or wireless network. Given the limited resource oftime slots, the scheduler at a base station must pick the appropriateuser at each slot according to certain rule(s). As can be readilyunderstood, packet transmissions of the selected user will add up to itsthroughput over time. Accordingly, an exemplary rule would be one thatmaximizes the sum of some utility functions, or the total “revenue”generated by each user's mean throughput. In light of the networkeconomy for elastic traffic of best-effort services, the utilityfunction would be increasing, strictly concave, and continuouslydifferentiable (see, e.g., S. Shenker, “Fundamental Design Issues ForThe Future Internet”, IEEE J. Select. Areas Commun., Vol. 13, No 7, pp.1176-1188, September 1995).

Accordingly, the scheduling problem may be formulated into a long-termoptimization problem under stationary and ergodic assumptions:$\begin{matrix}{{\max\limits_{U_{k}}{\sum\limits_{k = 1}^{K}\quad{U_{k}\left( {E\left\lbrack {{r_{k}(t)}1_{({{k^{*}{(t)}} = k})}} \right\rbrack} \right)}}} = {\max\limits_{\{{\overset{\rightharpoonup}{r}}_{k}\}}{\sum\limits_{k = 1}^{K}\quad{U_{k}\left( {\overset{\sim}{r}}_{k} \right)}}}} & \lbrack 3\rbrack\end{matrix}$

-   -   where r_(k)(t) denotes the attainable channel capacity at time        slot t; 1_((k*(t)=k)) is the instantaneous scheduling decision:        11, scheduler picks user k at slot t        $1_{({{k^{*}{(t)}} = k})} = \left\{ {\begin{matrix}        {1,} & {{scheduler}\quad{picks}\quad{user}\quad k\quad{at}\quad{slot}\quad t} \\        {0,} & {otherwise}        \end{matrix}.} \right.$

{tilde over (r)}_(k)=E[r_(k)(t)1_(k*(t)=k))] is the stationaryexpectation of the throughput of user k; U_(k)({tilde over (r)}_(k)) isthe utility function of the mean throughput. The optimization is takenover all possible solution set of {{tilde over (r)}_(k)}, which isdetermined by the scheduling decision making process under theconstraint of picking only one user per time slot:${\sum\limits_{k = 1}^{K}\quad 1_{({{k^{*}{(t)}} = k})}} = 1.$

Since r_(k)(t) is upper bounded by the MIMO channel capacity in equation[2], {tilde over (r)}_(k) is also upper bounded.

Under the stationary assumption, we can drop the time t in the above,but in practice we have to find the optimal scheduling decision methodwithout knowledge about the future channel. Additionally, the optimalscheduling method would need to solve a stochastic programming issuefacing high computational complexity and state explosion given a largenumber of users. Fortunately, we may advantageously use approximationsas follows.

In the time domain, the mean throughput can be estimated by anexponentially weighted moving average of instantaneous channel rate,e.g.,${{{\overset{\sim}{r}}_{k}\left( {t + 1} \right)} = {{\left( {1 - \frac{1}{t_{c}}} \right){{\overset{\sim}{r}}_{k}(t)}} + {\frac{1}{t_{c}}{r_{k}(t)}1_{({{k^{*}{(t)}} = k})}}}},$where t_(c) is the exponential filtering factor.

We can see that only the past decision affects the future. Accordingly,we define the asymptotic form of the utility function in optimizationas: $\begin{matrix}{U \equiv {\lim\limits_{t\rightarrow{+ \infty}}{U(t)}} \equiv {\lim\limits_{t\rightarrow{+ \infty}}{\sum\limits_{k = 1}^{K}\quad{{U_{k}\left( {{\overset{\sim}{r}}_{k}(t)} \right)}.}}}} & \lbrack 4\rbrack\end{matrix}$

As an approximation, we take the steepest gradient ascent of U(t) as theoptimized direction of the controlled system evolution under theconstraint${\sum\limits_{k = 1}^{K}\quad 1_{({{k^{*}{(t)}} = k})}} = 1.$

We now assume that the size of a time slot Δt is infinitesimal andt_(c)Δt is kept constant. The TDM-based scheduling then becomes afluid-flow process of continuous time t. Therefore, we have itsderivative in time domain as:$\frac{{dU}(t)}{dt} = {{\sum\limits_{k = 1}^{K}\quad{\frac{\partial{U_{k}\left( {{\overset{\sim}{r}}_{k}(t)} \right)}}{\partial{{\overset{\sim}{r}}_{k}(t)}}\frac{d{{\overset{\sim}{r}}_{k}(t)}}{dt}}} = {\sum\limits_{k = 1}^{K}\quad{\frac{{dU}_{k}\left( {{\overset{\sim}{r}}_{k}(t)} \right)}{\partial{{\overset{\sim}{r}}_{k}(t)}}{{{\overset{\sim}{r}}_{k}(t)}^{\prime}.}}}}$

Recalling the discrete-time {tilde over (r)}_(k)(t), we have${{\overset{\sim}{r}}_{k}\left( {t + {\Delta\quad t}} \right)} = {{\left( {1 - \frac{1}{t_{c}}} \right){{\overset{\sim}{r}}_{k}(t)}} + {\frac{1}{t_{c}}{r_{k}(t)}{1_{({{k^{*}{(t)}} = k})}.}}}$Therefore, {tilde over (r)}_(k)(t), is approximated by:$\frac{{{\overset{\sim}{r}}_{k}\left( {t + {\Delta\quad t}} \right)} - {{\overset{\sim}{r}}_{k}(t)}}{\Delta\quad t} = \frac{{{r_{k}(t)}1_{({{k^{*}{(t)}} = k})}} - {{\overset{\sim}{r}}_{k}(t)}}{t_{c}\Delta\quad t}$

It therefore follows that the steepest gradient ascent of U_(t) at timet is obtained by picking the user k*: $\begin{matrix}{k^{*} = {\arg\quad{\max\limits_{k}\left\{ {\sum\limits_{k = 1}^{K}\quad{\frac{\partial{U_{k}\left( {{\overset{\sim}{r}}_{k}(t)} \right)}}{\partial{{\overset{\sim}{r}}_{k}(t)}}\frac{{{r_{k}(t)}1_{({{k^{*}{(t)}} = k})}} - {{\overset{\sim}{r}}_{k}(t)}}{t_{c}\Delta\quad t}}} \right\}}}} & \lbrack 5\rbrack\end{matrix}$

This is our utility-based scheduling rule, where the utility function isdefined according to practical requirements. In practice, r_(k)(t) isthe instantaneous “supportable channel rate” fed back to the basestation through data rate control (DRC) channel—or other signaling—byindividual wireless terminal (k). {tilde over (r)}_(k)(t) may beestimated by exponential filtering at the base station. Note further,and in sharp contrast to optimization targets shown by X. Liu, E. K. P.Chong and N. B. Shroff, in a paper entitled “Opportunistic TransmissionScheduling With Resource-Sharing Constraints In Wireless Networks”,which appeared in IEEE J. Select. Areas Commun., vol 19, no 10, pp.2053-2064 in October 2001, in that our utility function depends uponlong-term per-user mean throughput whereas Liu et. al. defines an“instantaneous” utility function while trying to maximize theexpectations of the total utility under certain long-term time fractionconstraints. We maintain that long-term throughput is more relevant torevenue-generation in best-effort services.

To define the utility function according to the economic regulation suchas concavity and increasing monotonicity with respect to per-useraverage throughput, we note certain related strategies adopted in wired(Internet) networks that were described by F. Kelly, A. Maulloo, and D.Tan in an article entitled “Rate Control In Communication Networks:Shadow Prices, Proportional Fairness and Stability”, which appeared inthe Journal of the Operational Research Society, vol. 49, pp. 237-252,in July 1998; and a paper entitled “Fair End-To-End Window BasedCongestion Control”, authored by J. Mo and J. Walrand in IEEE/ACM Trans.Networking, vol 8, no. 5, pp. 556-567, October 2000; and proportionalfairness criteria which was proposed and subsequently extended to (p,α)proportionally fair. With this background in place, we may derive ourinventive scheduling method(s).

As can be appreciated, among the many fairness criteria associated withlink sharing, a popular one is the Max-Min fairness. In terms of ourproblem, this means the feasible set of mean throughput {{tilde over(r)}_(k)} of which any user i can not increase its mean throughput{tilde over (r)}_(i) without decreasing a smaller or equal {tilde over(r)}_(j). An attempt to achieve near-optimum Max-Min fairness amongTransmission Control Protocol (TCP) and User Datagram Protocol (UDP)users was made by A. Sang, H. Zhu and S. Q. Li in a paper entitled“Weighted Fairness Guarantee for Scalable Diffserv Assured Forwarding”,that appeared in Proc. IEEE Int. Conf. Commun, (ICC), pp. 2365-2369,June 2001. Both fairness criteria attempts to optimize the sum ofstrictly concave and increasing functions in the form of max${\left\{ {\overset{\sim}{r}}_{k} \right\}{\sum\limits_{k = 1}^{K}\quad{U_{k}\left( {\overset{\sim}{r}}_{k} \right)}}},$where the optimization constraint is the bottleneck link capacity.

In our notation, the (w,α) proportional fairness dictates that given apositive w=[w₁, . . . ,w_(k)] and a non-negative α, a vector {{tildeover (r)}_(k) ^(*)} is (w,α) proportionally fair if under the linksharing capacity constraint it satisfies $\begin{matrix}{{\sum\limits_{k = 1}^{K}\quad{w_{k}\frac{{\overset{\sim}{r}}_{k} - {\overset{\sim}{r}}_{k}^{*}}{{\overset{\sim}{r}}_{k}^{*a}}}} < 0} & \lbrack 6\rbrack\end{matrix}$for any other non-negative and feasible vector {{tilde over(r)}_(k)}under the same constraint. It is noted that such a {{tilde over(r)}_(k)} maximizes the utility function given by $\begin{matrix}{{U_{k}\left( {\overset{\sim}{r}}_{k} \right)} = {w_{k}\frac{{\overset{\sim}{r}}_{k}^{1 - a}}{1 - a}}} & \lbrack 7\rbrack\end{matrix}$where w_(k)>0, α≧0, and U_(k)(.) is a strictly concave and increasingfunction of {tilde over (r)}_(k)(t). Yet in our scenario, there is nostatic capacity constraint of link sharing among K users, but aconstraint on time slot sharing instead. Following our earlier logic,and adopting${{U_{k}\left( {\overset{\sim}{r}}_{k} \right)} = {w_{k}\frac{{\overset{\sim}{r}}_{k}^{1 - a}}{1 - a}}},$where w_(k) is the weight of user k in the total utility, we have thefollowing maximization target:${\sum\limits_{k = 1}^{K}\quad{\frac{w_{k}}{{{\overset{\sim}{r}}_{k}(t)}^{a}}\frac{{{r_{k}(t)}1_{({{k^{*}{(t)}} = k})}} - {{\overset{\sim}{r}}_{k}(t)}}{t_{c}\Delta\quad t}}} = {{\sum\limits_{k = 1}^{K}\quad{\frac{w_{k}}{t_{c}\Delta\quad t}\frac{r_{k}(t)}{{{\overset{\sim}{r}}_{k}(t)}^{a}}1_{({{k^{*}{(t)}} = k})}}} - {\sum\limits_{k = 1}^{K}\quad{\frac{w_{k}}{t_{c}\Delta\quad t}{{\overset{\sim}{r}}_{k}(t)}^{1 - a}}}}$Since {tilde over (r)}_(k)(t) as the mean throughput before time t isindependent of the instantaneous capacity r_(k)(t) and the schedulingdecision 1_((k*(t)=k)), we can ignore the second part of the aboveequation. Therefore, the maximization problem transforms into ourinventive scheduling method, which as we have indicated prior, we nameAlpha-Rule: $\begin{matrix}{k^{*} = {\arg\quad{\max\limits_{k}\left\{ {w_{k}\frac{r_{k}(t)}{{{\overset{\sim}{r}}_{k}(t)}^{a}}} \right\}}}} & \lbrack 8\rbrack\end{matrix}$

Advantageously, and as can now be readily appreciated by those skilledin the art, by varying the parameters w_(k) and α, we can get adifferent scheduling result as the circumstances may dictate.

When considering best-effort wireless data services, two metricscharacteristic of scheduling performance are of particular importance.Those metrics are throughput and fairness.

Throughput refers to the aggregate scheduling throughput which may berepresented by: $\begin{matrix}{r = {\sum\limits_{k = 1}^{K}\quad{\overset{\sim}{r}}_{k}}} & \lbrack 9\rbrack\end{matrix}$Fairness, refers to the per-user performance comparison. A fairnessindex may be defined as: $\begin{matrix}{F = \frac{\left( {\sum\limits_{k = 1}^{K}\quad x_{k}} \right)^{2}}{K{\sum\limits_{k = 1}^{K}\quad x_{k}^{2}}}} & \lbrack 10\rbrack\end{matrix}$where x_(k) denotes the per-user performance measure, such as theper-user time-fraction or per-user mean throughput {tilde over (r)}_(k).

As can be appreciated, F is a resource-based (time) or aperformance-based (throughput) index, indicative of fairness. It is acontinuous function, ranging between 0 and 1. Larger F is indicative ofgreater or better fairness. In particular, when F=1, the scheduler iscompletely fair as all x_(k) are equal. In contrast $F = \frac{1}{K}$is extremely unfair, as only one x_(k) is nonzero.

To further exhibit the flexibility of our inventive Alpha-Rule, considerthe situation when all users are equally weighted, i.e., w_(k)=1,∀k. Inthis situation, we have the following special cases of the method.

α=0: In this special case, the optimization target becomesmax_({{tilde over (r)}) _(k) _(})Σ_(k=1) ^(K){tilde over (r)}_(k). Byequation [8], the Alpha-Rule reduces to k*=argmax_(k){r_(k)(t)}; i.e.,the max-C/I method described earlier which always picks the user of thebest channel and starves the worst-channel users, for example, those whoare most remote from the base station. Clearly, this special casemaximizes throughput without much consideration to fairness.

α=1: In this special case, the optimization target is equivalent tomax_({{tilde over (r)}) _(k) _(})Σ_(k=1) ^(K)log{tilde over (r)}_(k).The Alpha-Rule then becomes${k^{*} = {\arg\quad{\max_{k}\left\{ \frac{r_{k}(t)}{{\overset{\sim}{r}}_{k}(t)} \right\}}}},$i.e., the Proportionally Fair (PF) scheduling described earlier. Recall,that the PF scheduling picks the user of the best ratio of channel rateto mean throughput. Accordingly, the PF scheduling asymptoticallyguarantees an equal sharing of time slots among all users, i.e., theresource-based fairness index is around 1.

α=2: In this special case the target is to minimize$k^{*} = {\arg\quad{\max_{k}{\left\{ \frac{r_{k}(t)}{{{\overset{\sim}{r}}_{k}(t)}^{2}} \right\}.}}}$As such, the rule minimizes the “potential delay” of all users. Inparticular, the resultant scheduling policy is represented by$\sum\limits_{k = 1}^{K}\quad{\frac{1}{{\overset{\sim}{r}}_{k}}.}$With such a rule, users of poorer channels tend to get more time slotsin order to reduce the summarized transmission delay of users with equalpacket size. As such, the aggregate throughput associated with thisspecial case is lower than PF and even round robin (RR) scheduling.

α→∞: In this special, extreme case, max-min fairness is achieved in thatthe scheduler equalizes the throughput of all users. Statedalternatively, the scheduler tends to pick the user associated with thesmallest mean throughput at each time slot. Consequently, a significantfraction of time is allocated to users of noisy channels. As should beapparent, this special case exhibits the lowest aggregate throughput ofall special cases.

Of further significance in any discussion of our inventive Alpha-Rule isa mention that the weight w_(k) can be used to differentiate users fromdifferent classes, or users in the same class but necessitating per-userrequirements for resource sharing and throughput. And while we haveassumed for the purposes of our discussion(s) that users of a systemutilizing our inventive Alpha-Rule are equally weighted, alternativeweighting methodologies would certainly complement our inventive method.

Lastly, as noted before, the α in our inventive Alpha-Rule as describedin equation [13] controls the overall scheduling performance and thetradeoff between aggregate throughput and per-user fairness. A larger αprovides more time slots to users of weaker channel(s). Consequently,increasing α naturally diminishes the total throughput. Given thismonotonic relationship, it should be readily apparent to those skilledin the art that a closed-loop tuning of α, based on online or real timemeasurements of r or F, may produce a desired effect.

Turning our attention now to FIG. 3, there is shown a flow chartdepicting our inventive Alpha-Rule method which is the subject of theinstant application. Specifically, and with reference to that FIG. 3, itis noted in 310 that our inventive Alpha-Rule operates at a Base Station(BS) or other device which schedules access to a shared network wheremultiple users are granted access through timeslots.

Continuing, a Base Station (BS) broadcasts a Pilot Signal for eachtimeslot in block 315 and, for each Mobile Station (MS) k=1, . . . K, inblock 320, a channel measurement of the pilot signal strength at each MSfor each timeslot is made in block 330, and provided to the channelcollecting statistics block of BS by all MSs using feedback channel 370,thereby producing current channel statistics for all mobile stations ata particular timeslot, r_(k)(t). This sub-process between blocks315-330, is performed continuously.

At block 380, past throughput for each mobile station is measured at thebase station, and then the current channel statistics for each time slotbeing continuously collected at block 370 are sorted at block 360according to our inventive Alpha-Rule.

The appropriate MS user is scheduled in block 350 and subsequentlytransmitted at block 340 while others are kept buffered or idled. Thisprocess between blocks 380-340 are continuously repeated as well.

Importantly, our inventive method can be tuned, as depicted by off-chartinput block 390, which provides Alpha-Rule updates or tuning.

With reference now to that FIG. 4 the flow chart depicted therein, it isnoted as before that two important components to our inventiveAlpha-Rule are the throughput and fairness components as identified inblock 410. As can be understood by inspection of the FIGURE, if both thethroughput and fairness exceed their targets, block 410 directs flowback to block 430, where our inventive Alpha-Rule assigns the user toreceive the particular time slot.

If, at block 440, it is determined that the throughput is less than itstarget and the fairness exceeds its target, Alpha (α) is decreased atblock 450 and the user for that particular timeslot is again determinedat block 430.

If, at block 460, it is determined that the throughput exceeds thetarget but the fairness does not meet its target, then Alpha (α) isincreased at block 470 before the user of a particular timeslot isdetermined at block 430.

Finally, if both the throughput and the fairness do not meet or exceedtheir targets at block 480, then the targets require adjustment which isperformed at block 490. This entire process depicted, is repeated foreach of the timeslots as depicted by block 495.

Of course, it will be understood by those skilled in the art that theforegoing is merely illustrative of the principles of this invention,and that various modifications can be made by those skilled in the artwithout departing from the scope and spirit of the invention, whichshall be limited by the scope of the claims appended hereto.

1. A method of determining which users, from a plurality of users,access to a communications system is to be provided, such access beingprovided to the plurality of users over a plurality of channels, themethod comprising the steps of: determining, for each of plurality ofchannels and for each of the plurality of users, a channel measurementfeedback characteristic; determining, for each of the plurality ofchannels and for each of the plurality of users, a past throughputcharacteristic; and determining, a user to be provided access accordingto the following relationship:$k^{*} = {\arg\quad{\max\limits_{k}\left\{ {w_{k}\frac{r_{k}(t)}{{{\overset{\sim}{r}}_{k}(t)}^{a}}} \right\}}}$where r_(k)(t) is the channel measurement feedback characteristic ofuser k; {tilde over (r)}_(k)(t) is the mean throughput of user k; w_(k)is a weight applied to each of the users; α is the alpha rule tuningparameter wherein α≠0 and α≠1; and k* is the selected user.
 2. Themethod according to claim 1 further comprising the steps of:determining, a throughput characteristic for the system; determining, afairness characteristic for the system; and adjusting α, as a result ofthe determined throughput characteristic and the determined fairnesscharacteristic.
 3. The method according to claim 2 further comprisingthe steps of: comparing, the determined throughput characteristic forthe system with a target throughput characteristic; comparing, thedetermined fairness characteristic for the system with a target fairnesscharacteristic.
 4. The method according to claim 3 wherein the adjustingstep further comprising the steps of: decrementing α, by a predeterminedamount, when the determined throughput characteristic for the system is≦ the target throughput characteristic and the determined fairnesscharacteristic for the system is ≧ the target fairness characteristic.5. The method according to claim 3 wherein the adjusting step furthercomprising the steps of: incrementing α, by a predetermined amount, whenthe determined throughput characteristic for the system is ≧ the targetthroughput characteristic and the determined fairness characteristic forthe system is ≦ the target fairness characteristic.
 6. The methodaccording to claim 3 wherein the adjusting step further comprising thesteps of: adjusting the targets, by a predetermined amount, when thedetermined throughput characteristic for the system is ≦ the targetthroughput characteristic and the determined fairness characteristic forthe system is ≦ the target fairness characteristic.
 7. The methodaccording to claim 3, wherein the throughput characteristic isdetermined according to the following relationship:$\overset{\sim}{R} = {\sum\limits_{k = 1}^{K}\quad{{\overset{\sim}{r}}_{k}(t)}}$where {tilde over (r)}_(k)(t) is the mean throughput of user k.
 8. Themethod according to claim 3, wherein the fairness characteristic isdetermined according to the following relationship:$\overset{\sim}{F} = \frac{\left( {\sum\limits_{k = 1}^{K}{{\overset{\sim}{r}}_{k}(t)}} \right)^{2}}{\left( {K\quad{\sum\limits_{k = 1}^{K}{{\overset{\sim}{r}}_{k}(t)}^{2}}} \right)}$where {tilde over (r)}_(k)(t) is the mean throughput of user k; and K isthe total number of users.
 9. The method according to claim 4, wherein ais decremented by a percentage of its present value.
 10. The methodaccording to claim 5, wherein a is incremented by a percentage of itspresent value.
 11. The method according to claim 9, wherein thepercentage that a is decremented by is between 0% and 100%.
 12. Themethod according to claim 10, wherein the percentage that a isincremented by is between 0% and 100%.
 13. The method according to claim2, wherein the adjusting of a is performed in real-time.